The Annals of Statistics

The jackknife estimate of variance of a Kaplan-Meier integral

Winfried Stute

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Abstract

Let $\hat{F}_n$ be the Kaplan-Meier estimator of a distribution function F computed from randomly censored data. It is known that, under certain integrability assumptions on a function $\varphi$, the Kaplan-Meier integral $\int \varphi d \hat{F}_n$, when properly standardized, is asymptotically normal. In this paper it is shown that, with probability 1, the jackknife estimate of variance consistently estimates the (limit) variance.

Article information

Source
Ann. Statist., Volume 24, Number 6 (1996), 2679-2704.

Dates
First available in Project Euclid: 16 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032181175

Digital Object Identifier
doi:10.1214/aos/1032181175

Mathematical Reviews number (MathSciNet)
MR1425974

Zentralblatt MATH identifier
0878.62027

Subjects
Primary: 62G05: Estimation 62G09: Resampling methods
Secondary: 62G30: Order statistics; empirical distribution functions 60G42: Martingales with discrete parameter

Keywords
Censored data Kaplan-Meier integral variance jackknife

Citation

Stute, Winfried. The jackknife estimate of variance of a Kaplan-Meier integral. Ann. Statist. 24 (1996), no. 6, 2679--2704. doi:10.1214/aos/1032181175. https://projecteuclid.org/euclid.aos/1032181175


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